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%I #3 Mar 31 2012 13:48:52
%S 1,0,1,1,2,3,3,1,0,2,2,2,2,3,5,5,5,5,2,0,3,3,3,3,3,3,4,7,7,7,7,7,7,3,
%T 0,4,4,4,4,4,4,4,4,5,9,9,9,9,9,9,9,9,4,0,5,5,5,5,5,5,5,5,5,5,6,11,11,
%U 11,11,11,11,11,11,11,11,5,0,6,6,6,6,6,6,6,6,6,6,6,6,7,13,13,13,13,13,13
%N Sequence of digits (least significant digit first) of A124797 (sums of cyclic permutations of 1...n written in base n+1).
%C Sequence A083956 becomes "unnatural" for n>9. It is easily seen that for n=2k, the sum of permutations A124797(n) is {k:n}0 in base n+1 where {k:n} means n times the digit k; while for n=2k+1 (>1), the sum is k{n:2k}{k+1} (again in base n+1). In particular, this number has n+1 digits (for n>1), such that the digits for A124797(n) start at place n(n+1)/2-1 (for n>1).
%e a(1)=1, the sum of cyclic permutations of 1;
%e a(2..4)=0,1,1 since 12 + 21 = 110 in base 3;
%e a(5..8)=2,3,3,1 since 123 + 231 + 312 = 1332 in base 4;
%e a(9..13)=0,2,2,2,2 since 1234 + 2341 + 3412 + 4123 = 22220 in base 5.
%p A124797 := n->(n+1)/2*((n+1)^n-1): map(op, [ 'convert(A124797(i),base,i+1)' $ i=1..20 ]);
%Y Cf. A083956, A124797.
%K base,easy,nonn
%O 1,5
%A _M. F. Hasler_, Nov 07 2006
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